The paper describes a modified scenario method for risk estimation of financial instruments. It is based on the scenario method proposed by Jamshidian F. and Zhu Y. allowing to significantly reduce computation time of risk indicators on large portfolios compared to the Monte Carlo method. It is proposed to change the way of choosing scenarios and points of approximating distribution. It allows to improve the quality of approximation. More than that, the new method makes possible to remove restrictions on the type of distribution of portfolio price factors allowing to expand the scope of its application. The comparison of VaR (value at risk) estimation using original and modified method was performed on a financial portfolio consisting of an interest rate swap for cases when the values of the price factors have normal distribution, gamma distribution and Student’s t-distribution.
Keywords:
Monte Carlo method, scenario simulation, interest rate swap, Value-at-Risk
It was proved earlier that product xy is a universal function for the class of linear functions depending on two arguments if k = 6l ± 1. In the paper we prove that there is no universal polynomials for the class of linear functions depending on two arguments for any k dividing three. Also we show that there is no universal
polynomials for the class of linear functions depending on three arguments for any even k. Thus the criterion of existence of universal polynomials for the class of linear functions is obtained.
Keywords:
generation, universal function, sum modulo, polynomial
The problem of applying erasure coding methods at the transport level to restore lost packets is considered. This will allow to avoid multiple retransmissions of the same packet, reduce data transmission delays, and waste of network resources. The basic idea behind erasure coding methods is to introduce redundancy into the transmitted data, which will allow the lost data to be recovered on the receiver side. The paper considers various erasure coding methods at the transport level, selects the most promising ones based on the computational complexity of the encoding and decoding algorithms, as well as the effect of redundancy on the data transmission delay and the transport connection loss level. The required level of redundancy in the selected error-correcting coding methods is given, depending on the requirements for the loss level in the transport connection and its quality characteristics.
Keywords:
quality of service, erasure code, transport level
For an isotropic stratified elastic strip we consider the Poincaré–Steklov operator that maps normal stresses into normal displacements on part of the boundary. A new variant of the algorithm is proposed for computing a transfer function of this operator. This variant is based on preconditioned conjugate gradient method.
